Positivity https://doi.org/10.1007/s11117-018-0588-z Positivity Statistical equi-equal convergence of positive linear operators 1 1 Fadime Dirik · Pınar Okçu Sahin ¸ Received: 14 February 2018 / Accepted: 22 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract Many researchers have been interested in the concept of statistical conver- gence because of the fact that it is stronger than the classical convergence. Also, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this paper we deﬁne a new type of statistical convergence by using the notions of equi-statistical convergence and statis- tical equal convergence to prove a Korovkin type theorem. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. After, we present an example in support of our deﬁnition and result presented in this paper. Finally, we also compute the rates of statistical equi-equal convergence of sequences of positive linear operators. Keywords Statistical equal convergence · Equi-statistical convergence · Positive linear operators · Korovkin theorem · Modulus of continuity Mathematics Subject Classiﬁcation 41A25 · 41A36 1 Introduction The notion of statistical convergence for sequences of real
Positivity – Springer Journals
Published: Jun 2, 2018
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